**A wave propagation method for three-dimensional hyperbolic
conservation laws
**

by Jan Olav Langseth and R. J. LeVeque,
*J. Comput. Phys.* 165 (2000) pp. 126-166.

**Abstract.**
A class of wave propagation algorithms for three-dimensional conservation
laws and other hyperbolic systems is developed. These unsplit finite
volume methods are based on solving one-dimensional Riemann problems
at the cell interfaces and applying flux-limiter functions to suppress
oscillations arising from second derivative terms. Waves emanating from
the Riemann problem are further split by solving Riemann problems in
the transverse directions to model cross-derivative terms. With proper
upwinding, a method that is stable for Courant numbers up to one can be
developed. Stability theory for three-dimensional algorithms is found
to be more subtle than in two dimensions and is studied in detail.
In particular we find that some methods which are unconditionally
unstable when no limiter is applied are (apparently) stabilized by the
limiter function and produce good looking results. Several computations
using the Euler equations are presented, including blast wave and complex
shock/vorticity problems. These algorithms are implemented in the CLAWPACK
software which is freely available.

Simulations to accompany this paper

**bibtex entry:**

@Article{jol-rjl:3d,

author = "J. O. Langseth and R. J. LeVeque",

title = "A wave-propagation method for three-dimensional
hyperbolic conservation laws",

journal = "J. Comput. Phys.",

volume = "165",

year = "2000",

pages = "126--166",

}